From September 2015 to September 2017, John Troutman McCrann, a high school math teacher, NBCT, and MfA Master Teacher Fellow in New York City, wrote about his quest to integrate inquiry- and performance-based learning into his instruction, and how these concepts might inform education policy. Follow him on Twitter: @JohnTroutMcCran

3 Tips for Guided Inquiry Math Lessons: The Ikea Effect

By John T. McCrann on
May 4, 2016 5:15 PM

My wife and I just bought our first home this winter. We have spent a lot of time this spring acquiring the furniture that we need to transition from a 400 square foot apartment to a three bedroom townhouse.

We've gotten furniture from family, yard sales, and a we have bought a handful of new things. Of all these, some of my favorite items are ones that we got from Ikea. I look at them and smile thinking of how I transformed them from slabs and screws into functioning furniture (insert the Tim "the Toolman" Taylor grunt here).

Social scientists have named the psychological phenomenon that creates my sense of pride. The "Ikea Effect," explains that "people attach greater value to things they built than if the very same product was built by someone else."

Math teachers can leverage this same psychological phenomenon through inquiry experiences in class.

My students show more and learn more from experiences in which they feel like they have been a part of the construction of the knowledge, and not simply a passive recipients.

This idea is, of course, not something I came up with. Dewey and Friere are my two favorite scholars on the value of inquiry to the educational process. One way to start a genuine inquiry cycle for those who are unfamiliar with the process might be to check out the work of "The Right Question Institute" (where you can find this step-by-step "how to")

True inquiry and authentic knowledge construction are great and should happen at times in every class; however, something I love about this "Ikea Effect" idea is that we don't need to experience "start-from-scratch" inquiry to realize its benefits. Guided or bounded inquiry has value as a means to engage students in owning material and developing deep ideas about it.

I'm not carpenter. I did not actually build anything in my house. It would be impractical for me to try create a shoe cabinet from a few two by fours.

And it would be equally ridiculous and impractical for me to ask my ninth grade students develop construct some mathematical ideas. My students cannot and should not reconstruct Euclid's Elements from a single postulate. Yet, this doesn't mean the ideas should simply be presented as "facts to be learned" either.

Ikea does a few things so that non-carpenters like myself can "construct" their furniture. They pre-drill holes in the wood, they provide would-be constructors with correctly sized tools which they'll need, and they write instructions for assembly which highlight the moves we should make as well as trouble spots where we are likely to go astray.

Math teachers can create analogous scaffolds to empower our students in the process of "constructing" knowledge.

Pre-drill holes: In the classroom, this means providing systems and structures that support students in the process of knowledge construction. Handouts should prompt students to observe a mathematical phenomenon with question like "What do you notice...?" Students should have plenty of room to express their understanding in different ways: drawing pictures, writing sentences, explaining verbally to the teacher or peers. Students should be set up in a way that will maximize their ability to engage with the problem and each other (for me this is usually, but not always, heterogeneous groups of four) and teachers should use tools like group roles and turn-and-talk strategies to create a context in which all students participate

Provide the correct tools: The right "tool" for mathematical knowledge construction could be a compass or ruler, but it might also mean giving students a crutch to support them as them move through a difficult part of the process (ex: a pre-scaled graph might help students graphing data in order to gain an understanding of amplitude changes in a sine curve). This is a delicate balancing act: I often struggle to select the "tools" which will give my students the help they are likely to need without providing so much that I destroy their opportunity to think and make sense. Teachers can set up students with online resources as tools to explore a phenomenon or relationship (National Library of Virtual Manipulatives, Geogebra, Desmos).

Create an instruction manual: Even with the right context and tools, students may need support putting things together in the right order (Quick note here: this is an important distinction between what I'm calling "true inquiry" and "guided/bounded inquiry." In the former I would not provide this kind of manual, in the latter I am guiding students toward a desired understanding so there needs to be more structure). In creating this "instructional manual," I try to anticipate where students will go wrong and head them off at the pass. This could be accomplished in the handout I give them or may be through moves in my facilitation of the group. My "instruction manual" might include collecting all students together to bring out misconceptions or sending ambassadors from one group that has gotten through a sticking point to another when they reach a similar spot.

Of course, Ikea furniture takes time to construct. Just as we couldn't fill every inch of our home with Ikea furniture, teachers (especially high school teachers who are required to march students through a curriculum which still does not emphasize depth of knowledge) cannot be expected to design this kind of inquiry experience every day.

Math policymakers should be working to solve this problem through curriculum reform. In the meantime, I will keep thinking about my shoe cabinet as I design lessons/curriculum, finding ways to give students the satisfaction of putting together mathematical knowledge.

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